The field of the invention is numerical control systems, particularly, numerical control systems having servotype position controls which employ rotary or linear resolver devices for indicating the position of the machine member being controlled.
Numerical control systems such as those described in U.S. Pat. No. 4,038,533 and (U.S. Ser. No. 970,959), U.S. Pat. No. 4,228,495 generate a sequence of position commands which direct the motion of a movable machine member through a series of moves. To obtain accuracy, a position sensor is coupled to the movable machine member and it generates a feedback signal that indicates actual machine member position. The position feedback signal is combined with the position commands to produce an error signal that is indicative of the instantaneous difference between the commanded position and the actual position of the controlled member. The servo loop is driven by this error signal and the position accuracy of the numerical control system is dependent upon the accuracy of the position sensor.
Rotary and linear resolvers have been used for many years as position sensors on numerical control systems. The resolver is excited by two periodic wave forms and it generates a third wave form which indicates the relative position of its movable member. In one common technique the amplitude of the generated wave form indicates position, and in a second technique, the phase of the generated wave form indicates position. An implementation of the amplitude technique is disclosed in U.S. Pat. No. 3,686,487 and implementations of the phase technique are disclosed in U.S. Pat. Nos. 4,023,085, 4,109,185, 4,134,106 and 4,204,257.
The accuracy of resolver position sensors is in large part a function of the accuracy of the periodic wave forms applied to them. When using the phase technique for example, the two resolver stator windings are ideally driven with pure sine waves of equal amplitude and in exact quadrature. The output signal on the resolver's rotor will then be a sine wave of the same frequency, but phase shifted by the resolver shaft angle. Stated mathematically, if the voltages applied to the resolver stators are Eo sin wt and Eo sin (wt-90.degree.)=-Eo cos wt; then the output on the rotor is: EQU E=(TR)Eo (sin wt cos .theta.-cos wt sin .theta.) or EQU E=(TR) (Eo) sin (wt-.theta.)
where:
(TR)=transformation ratio PA1 .theta.=resolver shaft angle PA1 w=angular frequency of stator wave forms PA1 .delta.=a small error in quadrature in radians. PA1 .DELTA..theta.=error in resolver shaft angle PA1 .delta.=quadrature error in radians PA1 .theta.=resolver shaft angle PA1 (TR)=transformation ratio PA1 E.sub.1 =peak value of one input wave form PA1 E.sub.2 =peak value of other input wave form PA1 .DELTA..theta.=error in resolver shaft angle PA1 .delta.=E.sub.2 /E.sub.1 -1 PA1 .theta.=resolver shaft angle PA1 .delta.=fractional amplitude of in-phase third harmonic.
Prior resolver systems using the phase technique determine the angle .theta. by detecting the crossover of the output sine wave and comparing it with the crossover of one of the input sine waves applied to the resolver.
The phase technique is accurate only if the applied wave forms are in exact quadrature, if the applied wave forms are of equal amplitude, and if there is no third harmonic distortion of the applied wave forms. If the applied stator wave forms are not exactly 90.degree. apart in phase, but are otherwise pure sine waves of the same amplitude and frequency; then the rotor output is given by: EQU E=(TR)Eo [sin wt cos .theta.-cos (wt+.delta.) sin .theta.]
where:
When the phase difference is determined by measuring the time difference between positive-going zero crossings, the resulting error in position feedback is as follows: EQU .DELTA..theta..perspectiveto..delta./2(COS 2.theta.-1) for small .delta.
where:
If the applied wave forms are not equal in amplitude then the output wave form is: EQU E=(TR)E.sub.1 sin wt Cos .theta.-(TR)E.sub.2 Cos wt sin .theta.
where:
When phase difference is determined by measuring the time difference between positive-going zero crossings, the resulting error in position feedback is as follows: EQU .DELTA..theta..perspectiveto..delta./2 sin 2.theta. for small .delta.
where:
Using input wave forms that are distorted in shape will also introduce error by shifting the zero crossing of the output wave form. Introducing third harmonic distortion will, for example, result in the following output wave form: EQU E=(TR)Eo [(sin wt+.delta. sin 3 wt) cos .theta.-(cos wt+.delta. cos 3 wt) sin .theta.] EQU E=(TR)Eo [sin (wt-.theta.)+.delta. sin (3 wt-.theta.]
where:
This harmonic distortion results in an error in resolver angle, .DELTA..theta., as follows: EQU .DELTA..theta..perspectiveto.-.delta. sin 2.theta. for small .delta.
Attempts have been made in prior resolver systems to minimize inaccuracies, but these have not been entirely successful. The input wave forms can be accurately generated using digital techniques, but the wave forms are converted to analog form before application to the resolver. The digital to analog converters and associated power amplifiers needed to accurately make this conversion are expensive and require considerable temperature compensation circuitry and continued manual adjustment to maintain the two wave forms in quadrature and at equal amplitude. In addition, zero crossing detection circuitry must be extremely stable with respect to temperature induced voltage offset drifts and phase shifts. These requirements have rendered the phase technique impractical for use in high resolution, high accuracy numerical control applications.